Alexander Polynomials of closed alternating braids

Abstract

We prove that the Alexander polynomials of certain families of alternating 4-braid knots satisfy Fox's Trapezoidal Conjecture. Moreover, we give explicit formulas for the signature and for the first 4 coefficients of the Alexander polynomial for a large family of alternating $n$-braid links and we verify that these 4 coefficients form a log-concave sequence.